I made this list by going through my twitter feed and looking for pieces that I retweeted. Problem: only the second half of the year would load in my browser. If you published an awesome post between January and June, it is not on this list.
Tape Diagrams, Big Feelings and other Predicaments of Teaching by Kim Van Duzer
I still don’t know whether tape diagrams are worth the Big Feelings they bring up. But what happened on Wednesday reminded me that all teaching and learning, math or otherwise, is emotional business.
There is too much focus on what is observable in a class period (bulletin boards, lesson plans, time management) and not enough on the culture and connections that teachers develop with and among their students.
The activity isn’t enough. Here are four different students who are all engaged in the same activity. Consider the following questions: What do you notice? What questions would you ask this student? What could you have offered this student prior to starting this activity?
Teaching linear functions for meaning by Kevin Hall
For years I’ve been rearranging the pieces of my linear functions unit like a jigsaw puzzle, trying to optimize comprehension for weaker students. Weaker students see math as a giant bag of disconnected steps to memorize, right? Changing that can require a cultural shift in the classroom that I’m not usually able to pull off.
Touching Calculus by Joe Schwartz
Edmund explained that what we would be creating was called a uniform tiling with curvature. He said that to understand what was happening mathematically we would need to use something called Differential Geometry, which is calculus in several dimensions. He said the equations would be quite complex.
Math Autobiographies by Kent Haines
I hate you.”
word games by Alan Jacobs
Here’s a useful habit to cultivate: Notice whenever people are leaning hard on a particular word or phrase, making it do a lot of work. Then try to formulate what they’re saying without using that terminology. The results can be illuminating.
If we want students to think about rate as something that is capable of varying, we should help students coordinate change in two different quantities, such as the height and volume of liquid in a filling bottle. Specifically, we should provide opportunities for students to think about one quantity as continuing to change while another quantity is changing along with it.
Whereas now that I’ve hormonally and surgically transitioned in the ways that felt right to me, I pass on a daily basis and I consider my transition to be a part of my past/history, so I disclose to new people about something that existed in my past. But I live my daily life as a man, and I don’t consider my daily experience to be different than any other man.
However, this has meant that I’ve become invisible.
Forging a New Identity by Heidi Fessenden
He’s mostly been known in school as someone who makes trouble and needs help. How will it feel to him to be known for a novel idea that is fodder for the mathematical thinking of 23 other kids?
Am I wrong? by Existential Quantifier
How do we as teachers fight this and train our students, especially girls, to have confidence in what they know? I want ALL of my students to be confident and proud. I never want to hear another girl say, “This is probably wrong but….”
Like a Weed: a 3-act task by Charlotte Sharpe
This task is a difference subtraction task, designed to elicit the question How much more?
Contemplate than Calculate by Brian P
One of the most beautiful aspects of this routine is that it goes beyond mere discovery learning. The goal isn’t for students to end up at the same strategy. The idea is to develop fluency and flexibility in their numeracy.
I’m still second guessing what I did, what I didn’t do, what I could have done. What was my pedagogical responsibility to these students, and how might my personal beliefs about religion factor into that decision?
Some of what I worked on this year
- For the last few years I’ve been frustrated with the limitations of tweeting/blogging. What about ideas that are longer than a post? My first attempt was a series of posts (on feedback) but that was a disappointing effort in a lot of ways. This year felt like a step in the right direction for me. I spent the first few months of 2016 working hard on “Not a Theory of Everything,” an essay about John Sweller and Cognitive Load Theory.
- Online eyeballs are tough to capture, though, and I got more interaction and responses from a blog post that used ideas from the essay than the essay itself. I don’t know what this means for the future of longform writing about teaching, but I was proud of the post: Cognitive Load Theory and Why Students are Answer-Obsessed.
- Before I wrote “Not a Theory of Everything,” I tried to write a longform piece that felt more like a weird mix of an essay and a blog post and a Lockhartian math book. I wrote this in Summer 2015, but never really could figure out how to make it work. I published it on my blog this year: On Visual Patterns and Feedback.
- Speaking of feedback, I wrapped up my Heinemann fellowship. My work in the fellowship involved working on feedback and writing about it, and I summarized my thoughts in three pieces: Beyond “Better-Luck-Next-Time” Feedback, Feedback — We Still Don’t Know What Works, and a Bonus Tracks from spill-over thoughts from those other two posts. (“We Still Don’t Know” was so hot that the Learning Scientists gave it a first-ever warning label.)
Reflections on 2016 Blogging and Speculations
When I started reading and writing about teaching back in 2010-2011, it seemed to me that the vast majority of math teachers were blogging about the activities they made or used. Most people were embedding slides or worksheets, or describing progressions of questions they had used. Dan, Kate, Sam, Mimi, Fouss, even Danielson in his way was doing this. This online community was oriented towards curriculum.
I think this is true, but I’ve done none of the work to check up on this belief so I know that it might be wrong. Like really really wrong. Another perfectly good explanation for why I might think that the community was oriented towards curriculum is that I was in my first few years of teaching and I saw everything through the lens of curriculum.
In the past few years, it seems to me that there’s been a shift. With the emergence of Desmos, Illustrative Mathematics and Mathalicious and (perhaps even more importantly) people like Graham and Robert and Andrew who pump out high-quality tasks, the landscape has changed. Resource sharing — remember all those virtual filing cabinets? — just isn’t the focus of the online community.
I think the MTBoS has gone through a phase where more and more of its members went into curricular development, and so the bar for resources-worth-sharing has been raised. To be sure, people are still sharing things on their blogs, but it has a different feel. I don’t know if I’m saying anything that Kate didn’t already say better in a post from last January:
This blog grew in popularity (and stays relatively popular even though I neglect it so) not because I invented something big and sexy but because it offered relatively easy swaps for practice worksheets and ugly, fresh-off-the-smartboard rewrites of high school lessons that made the kids do a tiny bit more thinking than usual.
The flipside of Kate’s observation is that people don’t really blog like this anymore.
And so teacher bloggers are looking for other ways to share that go beyond resource sharing. But this is hard, since so much of existing teacher-discourse is about resource sharing. (At least at the schools where I’ve taught.) It’s safer and easier to talk about pedagogy through the lens of resources.
I think of many of my favorite posts from 2016 — like Lisa and Grace’s above — and they focus on relationships and culture. But how do you talk about relationships and culture? This is hard stuff! It’s what, perhaps, teachers will be blogging about more in years to come, but it’s not easy to figure out how to talk about. The language isn’t always there for us in the way it is about designing a great task.
This is all speculation. I’ve said that enough times for you to not take this too seriously, right?
OK one last speculation. The elementary school bloggers have a head start on talking about culture and relationships. Joe, Heidi, Kim, Tracy — I loved posts they wrote this year partly because of their ability to talk sensibly about children, identity, feelings, relationship and culture. Secondary teachers might not yet have this language, but maybe we’ll learn it from our elementary colleagues.
In 2017, maybe we’ll see teachers find new ways to talk about the soft skills of teaching on their blogs.